quantum-ready

Multi-Temporal Interferometry (MTI) and Persistent Scatterer Interferometry (PSI) are key techniques in satellite Earth Observation for monitoring ground deformation with millimetre accuracy. Operational processing chains estimate line-of-sight displacement velocities from the dominant frequency of interferometric phase time series, extracted through Fast Fourier Transform analysis. As quantum computing technologies advance, investigating whether Quantum Fourier Transform algorithms might eventually complement or replace classical FFT kernels becomes increasingly relevant. In this thesis we investigate a QFT-based velocity estimator tailored to MTI time series. We construct a hybrid, “quantum-ready” workflow in which classical interferometric signals are amplitude-encoded into a quantum state, processed by a QFT circuit, and measured in the computational basis. Instead of reconstructing the full output spectrum, we focus on estimating only the most probable frequency bin by analysing the statistics of repeated projective measurements (shots). We introduce and compare several incremental estimators (mode with parabolic refinement, median, and mean) as a function of the total number of shots and of the zero-padding length. Validation encompasses 2005 real interferometric time series from the Cazzaso test site, acquired by Sentinel-1 C-band SAR and processed through operational industrial chains that provide FFT-based reference velocities. QFT-derived spectra are shown to reproduce the classical FFT peak locations, and the incremental mode and median estimators achieve better than millimetre-per-year agreement with operational velocities for realistic padding factors. These results provide a data-driven benchmark for the use of QFT in future quantum SAR/MTI processing pipelines, in line with the objectives of the Qu4EO (Quantum Computing for Earth Observation) project.

This research was developed in the context of the Qu4EO (Quantum Computing for Earth Observation) project, whose objective is to investigate the application of quantum computing paradigms to satellite Earth Observation data processing.